RBY OU What Are The Odds: Gengar vs Jynx.

The matchup between this pair of leads has been discussed quite a lot lately, and I figured it'd be a good idea to work out the odds. I'll look at 2 scenarios, in both cases assuming that the Gengar player's strategy is not to Explode turn 1. I'm also going to ignore 255s since in this scenario they should be fairly negligible (at worst impacting the 3rd significant figure).

Jynx tries to only Lovely Kiss Gengar:
Chance of Gengar successfully Sleeping Jynx without it waking up: 153/256*6/7=~18/35 =0.51..
Chance of Jynx successfully sleeping Gengar: 191/256*0.4=~3/10 = 0.3
Chance of nothing happening=13/70=0.1857..
Thus, the overall chances of:
Gengar victorious: ~12/19 = 63.1% (3 s.f.)
Jynx victorious: ~7/19 = 36.9% (3 s.f)

Jynx tries to KO Gengar with Psychic.
Jynx Psychic vs. Gengar: 159-188 (49.2 - 58.2%) -- 98.8% chance to 2HKO [becomes ~99.2% factoring in the possibility of a Spec drop, then ~99.3% when factoring in chance of a critical hit on the second hit]
Jynx Psychic vs. Gengar on a critical hit: 308-362 (95.3 - 112%) -- 71.8% chance to OHKO
We are going to work with the assumption that Gengar goes for Hypnosis at every opportunity.
T1 Jynx Asleep + Does not wake up: 459/896
T1 nothing happens: 153/1792
T1 Jynx does not Sleep: 103/256
-- Ignore the T1 does not happen by multiplying the other figures by 1792/1639 --
T1 Jynx Asleep | Gengar victorious: 918/1639
T1 Jynx not Asleep: 721/1639
-- Investigating the probabilities when Jynx does not fall asleep --
T1 Jynx Awake - Psychic critical hits and Gengar is KO'd | Jynx victorious : 0.718 * 721/1639 * 95/512 = 0.0586..
T1 Jynx Awake - Psychic critical hits and Gengar is not KO'd | Mark with x : (1 - 0.718) * 721/1639 * 95/512 = 0.0230..
T1 Jynx Awake - Psychic does not critical hit | Mark with y : 721/1639 * 417/512 = 0.3583..
-- Investigating x --
T2 Jynx Asleep | Gengar victorious: 918/1639 * P(X=x) = 0.0129..
T2 Jynx Awake and Gengar is KO'd | Jynx victorious: 721/1639 * P(X=x) = 0.0101..
-- Investigating y --
T2 Jynx Asleep | Gengar victorious: P(X=y) * 918/1639 = 0.2007..
T2 Jynx Awake and Gengar is KO'd | Jynx victorious: P(X=y) * 721/1639 * 0.993.. = 0.1565..
T2 Jynx Awake and Gengar is not KO'd | Go to Turn 3: P(X=y) * 721/1639 * 0.007.. = 0.0011
T3 Jynx Asleep | Gengar victorious: 0.0006..
T3 Jynx Awake and Gengar is KO'd | Jynx victorious: 0.0005..
Overall:
Gengar victorious: 77.4%
Jynx victorious: 22.6%

 

Hey this is pretty cool. I totally forgot about T1 wakes when I did my version of this, so this definitely makes your results more accurate than mine. Good stuff

 

Also a note, you can summare the ratios of Gar win:Jynx win as approximately 12:7 [LK], 7:2 [Psychic]

 

Time to do it with Egg, with its higher Special but lower critical hit rate!

Exeggutor tries to only Sleep Powder Gengar:
Chance of Gengar successfully sleeping Exeggutor without it waking up: 153/256*6/7=~18/35 =0.51..
Chance of Exeggutor successfully sleeping Gengar: 191/256*0.4=~3/10 = 0.3
Chance of nothing happening=13/70=0.1857..
Thus, the overall chances of:
Gengar victorious: ~12/19 = 63.1% (3 s.f.)
Exeggutor victorious: ~7/19 = 36.9% (3 s.f)

Exeggutor tries to KO Gengar with Psychic.
Exeggutor Psychic vs. Gengar: 190-224 (58.8 - 69.3%) -- guaranteed 2HKO
Exeggutor Psychic vs. Gengar on a critical hit: 372-438 (115.1 - 135.6%) -- guaranteed OHKO
We are going to work with the assumption that Gengar goes for Hypnosis at every opportunity.
T1 Exeggutor Asleep + Does not wake up: 459/896
T1 nothing happens: 153/1792
T1 Exeggutor does not Sleep: 103/256
-- Ignore the T1 does not happen by multiplying the other figures by 1792/1639 --
T1 Exeggutor Asleep | Gengar victorious: 918/1639
T1 Exeggutor not Asleep: 721/1639
-- Investigating the probabilities when Exeggutor does not fall asleep --
T1 Exeggutor Awake - Psychic critical hits and Gengar is KO'd | Exeggutor victorious : 721/1639 * 55/512 = 3605/76288 (=0.047255..)
T1 Exeggutor Awake - Psychic does not critical hit | Mark with x : 721/1639 * 457/512 = 0.39265..
-- Investigating x --
T2 Exeggutor Asleep | Gengar victorious: P(X=x) * 918/1639 = 0.2199..
T2 Exeggutor Awake and Gengar is KO'd | Exeggutor victorious: P(X=x) * 721/1639 = 0.1727..
Overall:
Gengar victorious: 78.002..%
Exeggutor victorious: 21.998..%

Otherwise, well approximated by 78% and 22% respectively.

 

Whoa, that's surprising. I know that's from 2015, but I'm playing RBY OU now and stumbled upon this!

With 60 Acc on Hypnosis vs 75 Acc Slee Powder/Lovely Kiss, it's very surprising that the majority of time Gengar win. This is amazing, thank you for sharing!